Simultaneously Formed Wedge‐Like Structures of Different Ion Species Deep in the Inner Magnetosphere

In this study, ion data from the Helium, Oxygen, Proton, and Electron (HOPE) spectrometers onboard Van Allen Probes reveal the existence of wedge‐like structures of O+, He+, and H+ ions deep in the inner magnetosphere. The behaviors of the wedge‐like structures in terms of temporal evolution, spatial distribution, upper energy limit, as well as dependence on solar wind and different geomagnetic indices are investigated from both event studies of several consecutive orbits on 3 February 2013 and the subsequent statistical analyses using 4 years of data. Unlike the dominant distribution at L=4 –8 in the dayside observed by the polar orbit satellites in previous studies, the wedge‐like structures deep in the equatorial plane of the inner magnetosphere are found mostly at the Mcllwain L shells of L=2 –5 and have a preferential location in the duskside and nightside. The O+ and He+ structures can extend to smaller L shells with higher upper energy limits than the H+ structures, while the upper energy limits of all these particle species show a similar variation tendency with respect to magnetic local time (MLT) and L. Observations indicate that these wedge‐like structures are probably attributed to fresh substorm injections from the outer region.


Introduction
The inner magnetosphere in the nearly dipole field is a highly dynamic region where relativistic radiation belt electrons, energetic ring current ions, and cold plasmaspheric particles overlap and interact with each other (e.g., Daglis et al., 1999;Darrouzet et al., 2009;Yue, Bortnik, Chen, et al., 2017;. It has been widely known that particles in the inner magnetosphere originate from both ionosphere and solar wind. Ions with source energies less than 1 eV can be accelerated and transported to the inner magnetosphere in a variety of ways (Keika et al., 2013). The azimuthal drift of trapped ions gives rise to the ring current, which consists of an energetic (several to hundreds of keV) component (e.g., Baker et al., 2001;Daglis et al., 1999;Gloeckler et al., 1985), and a sub-keV component (e.g., Collin et al., 1993;Yamauchi et al., 1996).
The energetic component is the primary carrier of the ring current, which increase significantly during magnetic storms and substorms (Kamide et al., 1998;Williams, 1985;Yue, Bortnik, Li, et al., 2019). Energetic ions from the plasma sheet will be freshly injected into the inner magnetosphere during geomagnetic activities, and exhibit some spectral features named after the shapes of energy bands in the energy-time spectrograms (Ferradas et al., 2016). These features include the "nose-like" structure (e.g., Ferradas et al., 2016;Smith & Hoffman, 1974), "trunk-like" structure (e.g., Zhang et al., 2015), and ion spectral gap (e.g., Kovrazhkin et al., 1999;Shirai et al., 1997). The formation of these spectral features are closely associated with the competition between the E × B drift and the magnetic gradient/curvature drift of injections from the nightside plasma sheet (Buzulukova et al., 2002;Ebihara et al., 2004;Ejiri et al., 1980;Shirai et al., 1997;Zhang et al., 2015).

10.1029/2020JA028192
This article is a companion to Zhou et al. (2020), https://doi.org/10.1029/ 2020JA028420.  energy for increasing latitude, (2) bridge-type with energy monotonically increasing with latitude but subsequently decreasing with latitude, and (3) reversed-wedge with decreasing energy for increasing latitude (Ebihara et al., 2001;Yamauchi et al., 2005). The wedge-like structures are detected by Cluster mainly in the proton channel but oxygen-dominant in the Freja observations (Yamauchi et al., 2005). They are preferentially located in the dayside (Ebihara et al., 2001;Yamauchi et al., 2005Yamauchi et al., , 2006 and commonly observed in the radial range of L = 4-8 (Ebihara et al., 2001). The finger-like structures were detected by Van Allen Probes around L = 2-3 near storm maximum and interpreted as the past injection (∼1 day before) from the nightside plasma sheet (Denton et al., 2016). Yamauchi et al. (2012Yamauchi et al. ( , 2014 observed some equatorially confined H + and He + ions with energy dispersion or dispersion-free features at the perigee (4-5 R E ) of Cluster spacecraft. It is an open question whether there are wedge-like ion structures deep in the inner magnetosphere and whether they will show any behaviors different from the polar orbit satellite (e.g., Cluster and Viking) observations. Van Allen Probes mission with two spacecraft (Probe A and Probe B) was launched into an ∼1.1 × 5.8 R E orbit with 10 • inclination and an orbital period of about 9 hr on August 2012 (Mauk et al., 2013), which provides a great opportunity for investigating the wedge-like structures in the equatorial plane of the inner magnetosphere. The Helium, Oxygen, Proton, and Electron (HOPE) spectrometer onboard Van Allen Probes can measure the 3-D distributions of the dominant ion species (O + , He + , and H + ) in the magnetosphere, which covers the energy range from ∼1 eV/q to 50 keV/q (Funsten et al., 2013).
The objective of this paper is to study the wedge-like structures of O + , He + , and H + in the inner magnetosphere on the aspect of temporal evolution, spatial distribution, upper energy velocity limit, and their dependence on solar wind and different geomagnetic indices, and to further explore the possible formation mechanism. This paper is organized as follows: Sections 2 and 3 present event observations and statistical results, respectively; discussion follows in section 4; section 5 summarizes the main findings in this study. Figure 1 shows the interplanetary conditions and geomagnetic indexes from 00:00 UT on 2 February 2013 to 00:00 UT on 4 February 2013. The interval marked by two vertical dashed lines corresponds to the time range from 00:00 to 16:00 UT on 3 February 2013 in Figure 2 when the wedge-like structures of different ion species were observed by Probe A and Probe B. Before this time interval, interplanetary magnetic field (IMF) B Z was oscillating around 0 nT in Figure 1a, the magnetic convection indicated by Kp index in Figure 1e was enhanced, and there were several consecutive substorms indicated by AE index in Figure 1f. In contrast, the solar wind velocity was constantly slow (400-500 km/s) in Figure 1b and there was no geomagnetic storm activities indicated by SYMH index in Figure 1d. All geomagnetic activities became relatively quiet during the interval. Figure 2 shows Probe A and Probe B observations in several consecutive orbits from 00:00 to 16:00 UT on 3 February 2013. Since the HOPE data are corrected with the measured spacecraft potential, there are some blank areas in the low energies (Sarno-Smith et al., 2016;. The orbits of Probe A (red line) and Probe B (blue line) in Figure 2a are labeled as Orbits I, II, III, and IV in the chronological order, with each one corresponding to a single inbound/outbound pass. In Figures 2c-2f, the energy spectrograms of differential fluxes (cm −2 s −1 sr −1 keV −1 ) of O + , He + , and H + show that there are simultaneously formed wedge-like structures (marked by the black arrows) in Orbit II (outbound pass of Probe A), which were not detected in the former inbound pass of Probe A. These structures were also observed in Orbit IV (inbound pass of Probe A) but disappeared in the next outbound pass. Probe B observations in Figures 2f-2h show that these wedge-like structures were also detected by Probe B in Orbit III (outbound pass), which became almost invisible in its next inbound pass, especially for H + . Observations in Figure 2 indicate that the wedge-like structures of O + , He + , and H + simultaneously emerged within a 1 hr frame and last for about 10 hr, and they are all located on the duskside-nightside. Figure 3 shows the energy fluxes (keV cm −2 s −1 sr −1 keV −1 ) of O + (first column), He + (second column), and H + (third column) as a function of L shell and energy in Orbits I-IV. The energy fluxes are assigned to the fixed grids (500 L values from L = 1 to L = 6 and 72 log-spaced energies from ∼1 eV to 50 keV). In Orbit I of Figure 3, there are two components for O + , He + , and H + : a low-energy population (approximately eV) in the plasmasphere and a high-energy population (several keV) as an extension of the energetic plasma sheet. In Orbit II of Figure 3, a new population with an energy-L shell dispersion feature emerged between the low-energy plasmasphere and the high-energy plasma sheet. The outer edge of the wedge-like structures connects to the plasmasphere population. The whole structures are isolated from the plasma sheet population but exhibit a variation tendency similar to the inner penetration boundary of the plasma sheet, especially for O + and H + . The black lines overlapped on the wedge-like structures in Orbits II and III of  Figure 3 represent the maximum intensity of the wedge-like structures, where it is required that the maximum intensity in each energy channel is 5 times larger than the average value within L = 1.5-2. The outer edges of the O + , He + , and H + structures are located in the same L shell and exhibit a dispersion-free feature below 100 eV. The inner edges of the O + and He + structures can extend to be closer to Earth with higher upper energy limits than H + . The similar phenomena were also observed in Orbit III of Figure 3 except that the He + structure further extended inward. In Orbit IV of Figure 3, small part of the wedge-like structures remains in Orbit IV, indicating that the structures are fading away due to charge exchange, Coulomb collision, and drift to elsewhere. Figure 4 shows the energy spectrogram and pitch angle distributions in some representative energy channels of O + , He + , and H + observed by Probe A from 00:00 to 16:00 UT on 3 February 2013. The pitch angle range from 0 • to 180 • is divided into 11 bins. The O + , He + , and H + ions in the wedge-like structures during the time intervals from 04:00 to 06:00 UT and from 10:00 to 12:00 UT exhibit a vertical pitch angle feature in each energy channel. These ions are dominantly distributed in the pitch angle range from 30 • to 150 • , indicating that the wedge-like structures consist of trapped ions. The same pitch angle features of the wedge-like structures were also observed by Probe B (not shown here).

Statistical Results
Four years of Van Allen Probes data from November 2012 to November 2016 are used to further investigate the wedge-like structures in the inner magnetosphere. Due to the orbit precession, Van Allen Probes can complete a 360 • scan of the equatorial plane for two times in 4 years. Events are selected according to the following steps: 1. Ion data from the HOPE spectrometer in each inbound/outbound pass of Probe A and Probe B are plotted in the same format as Figure 3. When there is a new population emerging between the low-energy plasmasphere and the high-energy plasma sheet just like observations as shown in Orbits II-IV of Figure 3, the plots of O + , He + , and H + will be picked out for further selection. 2. Obtain the maximum intensity of the wedge-like structures to determine the whole profile of the structures (e.g., the black lines in Orbits II and III of Figure 3). It is required that the maximum intensity in each energy channel is 5 times higher than the average value within L = 1.5-2. If the wedge-like structures can extend to the region of L = 1.5-2 in a few events, the maximum intensity in this region should be 5 times higher than the average value within L = 1.1-1.5. 3. Pick out the events that the whole profile of the O + , He + , and H + structures can cover at least five consecutive energy channels, and there is at least one ion species among O + , He + , and H + exhibiting an energy dispersion feature over a radial extension of 0.5 L shell (to exclude the finger-like structure in Denton et al., 2016).
According to the aforementioned steps and criteria, we obtain about 240 events in total. Figure 5a presents the event occurrence rate as a function of MLT (magnetic local time). To eliminate the influence from Van Allen Probes' orbits, the event occurrence rate is defined as the ratio of the observational time of events to the whole observational time of Probe A and Probe B from November 2012 to November 2016. The whole structure (first column), the outer (second column), and inner edges (third column) of the O + , He + , and H + structures exhibit a dominant distribution from MLT = 16 through MLT = 24 to MLT = 4 with a peak around MLT = 21. Here the whole structure refers to the maximum intensity profile of the wedge-like structures obtained via the aforementioned steps, and the outer and inner edges are the endpoints of each profile at the largest and smallest L shells, respectively. It indicates that the wedge-like structures in the inner magnetosphere have a preferential location in the duskside and nightside. Figure 5b presents the normalized event occurrence rate of the whole structure, the outer and inner edges as a function of L shell.

Spatial Distributions
In the radial direction, the whole structure of O + , He + , and H + is mainly distributed within L = 2-5 with a peak around L = 3.5 and the outer edge is commonly observed within L = 3-5 with a peak around L = 4. The inner edge of the O + and He + structures is mainly distributed at L = 2-3.5 while they are dominantly at L = 2.5-4.5 for H + . These results present that the wedge-like structures of O + and He + can extend to smaller L shells than H + . Figure 6 shows the upper energy limits of the O + , He + , and H + structures as a function of event number. The horizontal axis is logarithmic, but the space between two contiguous ticks is divided into nine equally sized

Dependence on V SW , P dyn , and Different Geomagnetic Indices
Here we investigate the relation between the occurrence of the wedge-like structures deep in the inner magnetosphere and solar wind velocity (V SW ), solar wind dynamic pressure (P dyn ), |SYMH|, Kp, and AE indices (accessed through the OMNIweb database). Figure 8 shows event occurrence for four ranges of these parameters. Blue and red colors represent that the maximum values of parameters are taken from the intervals of two orbit period (∼18 hr) before the event and from the interval of one orbit period (∼9 hr) during the event, respectively. In Figures 8a and 8b, most events occur under slow solar wind velocities (V SW = 400-600 km/s) and low solar wind dynamic pressures (P dyn < 4 nPa). Figures 8c and 8d present that the wedge-like structures are commonly observed when |SYMH|< 40 nT and Kp < 4, indicating that their occurrence is not associated with geomagnetic storm activities. The result in Figure 8d shows that event occurrence increases with larger AE index and AE is larger than 400 nT in most events. It indicates that the wedge-like structures are closely related to substorm activities.

Discussion
The measurements in Figures 2-8 have presented the temporal evolution of the simultaneously formed wedge-like structures of O + , He + , and H + , pitch angle feature, spatial distribution in the radial and azimuthal directions, upper energy limit, and their dependence on solar wind and different geomagnetic indices. To explore the ion source and the possible forming mechanisms, here we hypothesize three possible origins of the wedge-like structure: (1) direct escape of ionospheric ions, (2) energization of the local plasmasphere population, and (3) drift of injections from the outer region. The ionospheric outflows typically in the field-aligned feature can form energy-time or energy-L shell dispersions due to the time-of-flight effect (Quinn & McIlwain, 1979) or the velocity filter effect (Winningham et al., 1984). However, although outflows can be energized up to tens of keV in the inner magnetosphere (Chaston et al., 2015;Yue, Bortnik, Zou, et al., 2019), both effects are not available in the explanation of the wedge-like structure in this study because Van Allen Probe observations in Figure 4 show that the wedge-like structures consist of the trapped ions rather than outflows.
Observations in Figure 2 present that the wedge-like structures are connected to the plasmasphere at the outer edge but isolated from the plasma sheet. Can the wedge-like structure be formed due to energization of the local plasmasphere population (e.g., via wave-particle interactions or the impulsive electric field)? Previous observations have demonstrated that cold plasmaspheric ions can be heated up to hundreds of eV by ultralow frequency (ULF) waves due to the E × B effect (Ren, 2019;Yue et al., 2016), and cold electrons can be rapidly accelerated via drift-bounce resonance with the poloidal-mode electric field component (Ren et al., 2017(Ren et al., , 2018. But the radial distribution of the wedge-like structures is inconsistent with ULF waves, which are commonly observed outside the plasmapause (L > 4) (Dai et al., 2015;Liu et al., 2009;Ren et al., 2019). Similarly, EMIC waves can impart energy to cold ions over the energy range from approximately eV to tens of eV (Fuselier & Anderson, 1996;Gary et al., 1995;Ma et al., 2019) but have a preferential location in the dayside outer magnetosphere with the occurrence probability increasing for larger L shell (Anderson et al., 1992;Min et al., 2012). The interplanetary shock (IP)-induced impulsive electric field with the westward component can propagate inward across the magnetic field lines (Zong et al., 2009) and cause the energization of cold ions (Yue et al., 2016;Zong et al., 2012). But both event observation in Figure 1 and statistical results in Figure 8 show that there are no IP shocks in the events and no impulsive electric fields propagating along with the wedge-like structure (not shown here). Besides, it is  Blue and red colors represent that the maximum values of parameters are taken from the interval of two orbit periods (∼18 hr) before the event and from the interval of one orbit period (∼9 hr) during the event, respectively. uncertain how wave-particle interactions and IP shock-induced electric fields can lead to the energy-L shell dispersion feature.
The last scenario is drift of injections from the outer region. The measurements in Figure 3 show that the profile of the wedge-like structures exhibits a variation tendency similar to the inner penetration boundaries of the plasma sheet, indicating that they are both controlled by the combined effect of convection, corotation, and magnetic gradient/curvature drifts. There are several consecutive substorm activities before the appearance of the wedge-like structures in Figures 1 and 2, and the statistical analyses in Figure 8 present that there is a positive correlation between the event number and AE index before the events. These aforementioned observations indicate that the wedge-like structures deep in the inner magnetosphere are probably related to substorm activities. In our companion paper of (Zhou et al., 2020), we reproduced the wedge-like structures in Figure 2 using a particle-tracing model, and the model suggests that these structures are attributed to the adiabatic motion of the substorm injections drifting from the outer region in the nightside. To further investigate the possibility that the wedge-like structures in the inner magnetosphere can originate from the outer region, we plot the magnetic momentum-time spectrograms of the phase space density observed by Probe A from 00:00 to 16:00 UT on 3 February 2013 (see the supporting information in Figure S1). The phase space densities of the wedge-like structures are comparable to those at the apogee of Probe A orbit in the same magnetic momentum.
In the observations from the polar orbit satellites (e.g., Viking and Cluster) (e.g., Ebihara et al., 2001;Yamauchi et al., 2005), the wedge-like structures have a preferential location in the dayside within L = 4-8, which were successfully reconstructed as the signature of injections drifting over 10 hr from the nighside plasma sheet in Ebihara et al. (2001). As shown in Figure 4a of Zhou et al. (2020), the injections from the nighside travel along the open drift paths through dawnside/duskside to reach dayside. As L decreases in the dayside, it will take a longer drift time for injections to reach dayside (especially the afternoon sector) because the drift speed becomes smaller. It means that the injected ions in smaller L shells are more likely to be lost due to charge exchange and Coulomb collision before they reach dayside. This is probably the reason why the wedge-like structures deep in the inner magnetosphere are rarely observed in the dayside, as shown in Figure 5a. In the scenario of Zhou et al. (2020), the drift velocity of injected ions depends on particle energy and charge rather than particle mass. Therefore, the differences of O + and He + in comparison with H + in Figures 3-6 are not related to the formation mechanism of the wedge-like structure. The differences are probably due to (1) the lifetime of H + is much lower than O + and He + due to Coulomb collision and charge exchange (Fok et al., 1991) and (2) when the high-energy part of the H + structures is close to the flux background deep in the inner magnetosphere, it will be difficult to distinguish them.

Conclusion
We have investigated the wedge-like structures of O + , He + , and H + in the inner magnetosphere using four years of data from the HOPE spectrometers onboard Van Allen Probes. The main findings are listed as follows: 1. Event observations on 3 February 2013 present that the wedge-like structures of O + , He + , and H + were simultaneously detected by both Probe A and Probe B. The outer edges of the structures connects to the plasmasphere and exhibit a dispersion-free feature below 100 eV. The higher-energy part of the structure extends to smaller L shells monochromatically with increasing energy. The whole structure is isolated from the plasma sheet, but its profile shows a variation tendency similar to the inner penetration boundary of the plasma sheet, indicating that they are both controlled by the convection and corotation electric fields, and the magnetic gradient/curvature. The inner edge of the O + and He + structures can extend to be closer to Earth with higher upper energy limits than H + . The wedge-like structures consist of trapped ions rather than field-aligned outflows. Observations in several consecutive orbits indicate that the wedge-like structures emerged within 1 hr frame and faded away in about 10 hr. 2. Statistical results from 4 years of data show the spatial distributions and the upper energy limits of the wedge-like structures in the inner magnetosphere. In terms of azimuthal distribution, not only the whole structure but also the outer and inner edges are commonly observed from MLT = 18 through MLT = 24 to MLT = 4 with a peak distribution around MLT = 21. In the radial direction, the whole structure is mainly distributed within L = 2-5 with a peak around L = 3.5, the outer edge is mainly within L = 3-5 with a peak around L = 4, and the inner edge of the O + and He + structures is mainly at L = 2-3.5, whereas it is mainly at L = 2.5-4.5 for H + . The upper energy limits of O + , He + , and H + as a function of event number are mainly in the energy range of 0.5-30, 0.1-30, and 0.05-5 keV, respectively. And there are two peaks at 1 and 10 keV for both O + and He + while they are at 0.1 and 1 keV for H + . The upper energy limits of all these particles species display a decreasing tendency with respect to MLT in the range of MLT ∼ 16-24 and L shell. 3. Events mainly occur under the condition of slow solar wind velocities (V SW = 400-600 km/s) and low solar wind dynamic pressures (P dyn < 4 nPa). |SYMH| is lower than 40 nT in most events. Event occurrence increases for larger AE index and AE > 400 nT in most events, indicating that the wedge-like structures are closely related to substorm activities.
In previous studies, observations from the polar orbit satellites (e.g., Cluster and Viking) show the wedge-like structures are commonly observed at the L shells of L = 4-8 in the dayside (Ebihara et al., 2001;Yamauchi et al., 2005), which are interpreted as the signature of injections penetrating from the nightside plasma sheet (Ebihara et al., 2001). Observations in this study also indicate that the formation of the wedge-like structure in the inner magnetosphere is probably attributed to substorm injections drifting from the outer region. But the wedge-like structures in the equatorial plane of the inner magnetosphere have a preferential location within L = 2-5 in the duskside and nightside. In the future work, it deserves to further investigate how the wedge-like structures deep in the inner magnetosphere form and their possible link with the wedge-like structures in the outer regions (Ebihara et al., 2001;Yamauchi et al., 2005), the finger-like structure (Denton et al., 2016) and some other solitary structures (Yamauchi et al., 2012(Yamauchi et al., , 2014.